Many potential uses exist for information relating to the electrical conductivity and the permeability of porous rocks. In petroleum geophysics, the electrical conductivity is related to the oil saturation in a reservoir through the use of the Archie's Law relationship. The permeability is used to estimate the producibility of a reservoir or the facility with which oil may be extracted from a reservoir. The present invention advances the state of the art by providing an accurate method for predicting such pore-dependent properties as electrical conductivity and permeability using nonwetting fluid intrusion measurements.
The methods of the present invention are not restricted to porous rocks, but may find application to many porous materials that have a pore structure with a broad distribution of pore sizes. For example, catalyst support materials are microporous solids containing pores not unlike those in rocks. The methods described herein may be used to predict conductivity and permeability in such porous catalysts. Similarly, the methods may be used to predict the permeability and conductivity of porous electrode materials used in battery technology.
It has long been recognized that there is a relationship between capillary pressure or mercury intrusion curves and permeability. The paper "Capillary Behavior in Porous Solids," by Leverett (M. C. Leverett, Trans. AIME, 142, pp. 152-169 (1941)) in the early 1940's laid out one possible relation between capillary pressure and permeability. The pioneering work of this researcher is still in wide-spread use. In 1949, Purcell ("Capillary Pressures-Their Measurement Using Mercury and the Calculation of Permeability Therefrom," W. R. Purcell, Pet Trans. AIME, 186, pp. 39-48 (1949)) described a probable relationship between permeability and mercury intrusion and specifically pointed out that if one could make such an association then one could determine permeability from measurements on mud log cuttings. A more recent attempt to predict permeability from capillary pressure curves is disclosed in B. F. Swanson's paper entitled "A Simple Correlation Between Permeabilities and Mercury Capillary Pressures," J. Pet. Technol., pp 2498-2504 (Dec. 1981), which describes a variation on conventional predictions in which the ratio of the pore volume filled by mercury to the pore pressure is maximized. Most recently, T. Hagiwara, in the paper "Archie's m for Permeability," SPE Paper 13100 (1984)) extended the B. F. Swanson prediction to include an electrical conductivity measurement in the permeability prediction. Each of these previous attempts to predict permeability or conductivity has been moderately successful. However, each of these methods is semi-empirical, in the sense that the relationship between capillary pressure and permeability or electrical conductivity is basically determined by empirical relationships involving adjustable parameters in the equations relating the various physical parameters.
U.S. Pat. No. 4,211,106, issued July 8, 1980 to B. F. Swanson describes a method and means of predicting permeability from mercury capillary pressure measurements. A nomogram is applied to the capillary pressure data in accordance with the empirical model described in the above cited 1981 paper by Swanson. U.S. Pat. No. 4,211,106 discloses a method based on the empirical nomogram technique. It also describes an apparatus including means for measuring the pressure and volume of mercury inserted into a sample of 1 cc volume or less.
The present invention is very different from the prior art in several essential ways. Most importantly, the method of the present invention is a quantitatively explicit means for determining both the electrical conductivity formation factor and the absolute permeability of a porous medium. The conductivity and permeability are determined with no empirically adjustable parameters. The prior art does not disclose how to determine both conductivity and permeability from a single set of measured capillary pressure data, and the prior art requires use of empirical fitting parameters that could, in general, be different for every porous material.